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Supplementary Material
Title: Risk and protective factors for the development of depressive symptoms in children and
adolescents: results of the BELLA longitudinal study
Journal: Journal of European Child and Adolescent Psychiatry
Authors: Fionna Klasen, Christiane Otto, Levente Kriston, Praveetha Patalay, Robert Schlack,
Ulrike Ravens-Sieberer & the BELLA study group
Corresponding author: Fionna Klasen, University Medical Center Hamburg-Eppendorf, Department of Child and Adolescent Psychiatry, Psychotherapy, and Psychosomatics, Martinistrasse 52, D - 20246 Hamburg, Germany, email: f.klasen@uke.de
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Calculation and evaluation of latent growth models
For calculating LGMs, robust maximum-likelihood (MLR) estimation method was
used, which is a full-information maximum-likelihood technique. Since intervals between
points of data assessment were one year each, equidistant time scores were set in LGMs (the
slope quantifies the amount of change in the corresponding variable over one year). Further,
we assumed linear growth in each model, but we additionally tested for potential improvement
including a quadratic term. To compare models with and without additional shape factor, model
fit according to the Akaike information criterion (AIC) [1], the correlation between intercept
and slope, as well as residual variances were used. For final LGMs means and variances of
intercepts and slopes were calculated and the fit was evaluated according to the Root Mean
Square Error of Approximation (RMSEA) [2] and the Comparative Fit Index (CFI) [3].
Analyses revealed that the inclusion of an additional shape factor lead to no substantial
improvement in model fit (please see Supplementary Table 2; e.g. for the SCL-S-9 the linear
growth model had an AIC of 4,987.63 and the model with additional shape factor had an AIC
of 4,980.59). Correlations between intercepts and slopes as well as residual variances also differed only marginally, if at all, comparing models with linear growth to models with additional
shape factor (e.g. for SCL-S-9 models correlations between intercept and slope were -0.014
versus -0.015, residual variances hardly differed). For final LGMs, intercepts for all variables
had significant means and variances (see Supplementary Table 3). For the slopes average
change was significant for all variables, but the variance in depressive symptoms (p=.095) or
parental mental health problems (p=.283) was not significant. The fit of the model for depressive symptoms was good considering both indices (Chi²<0.001; p=0.9916; Degrees of Freedom
(df)=1; RMSEA<0.001; 90%-Confidence interval (90%-CI) for RMSEA=0.000-0.000;
CFI~1.000). For parental mental health problems, model fit was nearly acceptable considering
the Confidence interval for the RMSEA, but clearly acceptable according to the CFI
(Chi²=10.172; p=0.0014; df=1; RMSEA=0.075; 90%-CI for RMSEA=0.038-0.119;
CFI=0.984). For self-efficacy model fit was good due to both indices (Chi²=0.096; p=0.7564;
df=1; RMSEA<0.001; 90%-CI for RMSEA=0.000-0.000; CFI~1.000), but for family climate
an acceptable fit due to the RMSEA and a good fit based on the CFI were found (Chi²=1.519;
p=0.2178; df=1; RMSEA=0.018; 90%-CI for RMSEA=0.000-0.071; CFI=0.999). For social
support, model fit was close to acceptable, slightly beyond the limits reported for the estimate
of the RMSEA and the CFI (Chi²=12.023; p=0.0005; df=1; RMSEA=0.082; 90%-CI for
RMSEA=0.045-0.126; CFI=0.973). Overall, the fit of the LGMs used in the present study
ranged from nearly acceptable to good.
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Supplementary Table 1. Descriptive data of used measures in the analysed sample
Baseline
n
Socio-economic data
Gender
1-year follow-up
n
% (n)
[mean (SD)]
2-year follow-up
n
% (n)
[mean (SD)]
1,643
Female
50.6 (832)
Age (in years)
1,643
Socio-economic status2
1,643
[13.92 (2.003)]
Low
24.1 (396)
Middle
49.8 (819)
High
26.0 (428)
Depressive symptoms
Participants with depressive symptoms3
Depressive symptoms
Risk factor
Parents with mental health problems4
% (n)
[Mean (SD1)]
1,617
16.9 (273)
[9.85 (6.913)]
1,220
15.2 (185)
[9.39 (6.908)]
1,188
13.7 (163)
[9.13 (7.42)]
1,625
8.2 (133)
1,257
8.4 (106)
1,220
6.1 (75)
Parental mental health problems
[0.61 (0.531)]
[0.59 (0.532)]
[0.51 (0.511)]
Protective factors
Self-efficacy
1,616
[2.13 (0.382)]
1,217
[2.15 (0.436)]
1,188
[2.17 (0.406)]
Family climate
1,627
[1.83 (0.530)]
1,181
[1.84 (0.522)]
992
[1.80 (0.528)]
Social support
1,625
[3.12 (0.742)]
1,185
[3.30 (0.669)]
997
[3.32 (0.647)]
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SD=standard deviation;
2
The Winkler-index was used to categorise participants into groups with low (scores from 3 to 8), middle (9 to 14) or high (15 to 21) socio-economic status (Winkler et al.[4], Lange et al. [5]);
3
The sum-score of the CES-DC ranging from 0-60 was used to differentiate between participants with and without depressive symptoms using the published cutoff of 16 and above suitable to screen for major
depressive disorder (Fendrich et al. [6]);
4
The mean of the SCL-S-9 ranging from 0 to 4 was used to differentiate between participants with or without parental mental health problems according to published reference data using the cutoff of the mean
of the reference sample plus two standard deviations or a higher score as indicator for given mental health problems (Klaghofer et al. [7]).
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Supplementary Table 2. Comparison of models with linear growth to models with additional shapefactor
Models with linear growth
AIC2
Construct
Depressive symptoms
Risk factor
Parental mental health problems
Protective factors
Self-efficacy
Family climate
Social support
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correlation
residual variances
models with additional shape factor1
AIC
correlation
of intercept
of intercept
and slope
and slope
residual variances
2,6373.57
-1.978
19.530/22.183/24.092
2,6375.57
-1.981
19.526/22.188/24.077
4,987.63
-0.014
0.084/0.107/0.090
4,980.59
-0.015
0.084/0.107/0.089
3,301.77
4,828.26
7,269.57
-0.014
-0.026
-0.045
0.048/0.097/0.029
0.089/0.098/0.042
0.243/0.207/0.125
3,303.67
4,828.75
7,256.50
-0.014
-0.026
-0.045
0.048/0.097/0.029
0.090/0.098/0.042
0.243/0.204/0.126
Including a quadratic term with a variance of 0; 2 Akaike information criterion [1].
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Supplementary Table 3. Intercepts and slopes of latent growth models
Intercept
slope
Construct
Measure [range of raw scores]
mean
variance
mean
variance
Depressive symptoms
CES-DC1 [0–60]
9.845***
28.214***
-0.313**
3.014
SCL-S-92 [0-4]
0.615***
0.198***
-0.048***
0.009
Self-efficacy
GSE3 [0-3]
2.135***
0.098***
0.019***
0.024***
Family climate
FCS4 [0-3]
1.836***
0.192***
-0.020**
0.038***
Social support
SSS-short5 [0-4]
3.139***
0.296***
0.099**
0.046***
Risk factor
Parental mental health problems
Protective factors
Latent growth models were calculated assuming linear growth; ** p≤.01; *** p≤.001;
1
CES-DC=Center for Epidemiologic Studies Depression Scale (Radloff et al. [8], Barkmann et al. [9]);
2
SCL-S-9=Symptom-Check List Shortversion-9 (Klaghofer et al. [7]);
3
GSE=General Self-Efficacy Scale (Schwarzer et al. [10,11]);
4
FCS=Family Climate Scale (Schneewind et al. [12]);
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SSS-short=Eight items of the Social Support Survey (Donald et al. [13]).
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Supplementary Table 4. Self-efficacy moderating the association between parental mental health problems and depressive symptoms of children and adolescents
Regression Model A11
regression Model B12
predicting initial depressive
predicting change in depres-
symptoms
sive symptoms
b
β
p
b
<.001
-0.330
β
p
Constant
9.191
<.001
Female
1.300
.146
<.001
0.030
.021
.385
Age (in years at baseline)
0.309
.139
<.001
-0.007
-.021
.393
Socio-economic status (at baseline)
-0.058
-.055
.013
0.008
.046
.059
2.107
.189
<.001
0.127
.070
.012
0.999
.053
.055
0.002
.001
.979
-1.467
-.210
<.001
0.018
.003
.922
Change in parental mental health problems (slope) by change in self-efficacy (slope)
3.018
.018
.494
Initial parental mental health problems (intercept) by change in self-efficacy (slope)
-0.127
-.008
.773
Change in parental mental health problems (slope) by initial self-efficacy (intercept)
2.363
.033
.241
Risk factor
Initial parental mental health problems (intercept)
Change in parental mental health problems (slope)
Protective factors
Initial self-efficacy (intercept)
-5.950
-.356
<.001
Change in self-efficacy (slope)
Interactions between risk and protective factors
Initial parental mental health problems (intercept) by initial self-efficacy (intercept)
1
0.514
Linear regression Model A1 (n=1,643); model fit: R²=.230; F=81.270; 2 linear regression Model B1 (n=1,643); model fit: R²=.053; F=8.233;
b=unstandardized regression coefficient; β=standardized regression coefficient
.012
.568
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Supplementary Table 5. Family climate moderating the association between parental mental health problems and depressive symptoms of
children and adolescents
Regression Model A21
regression Model B22
predicting initial depressive
predicting change in depres-
symptoms
sive symptoms
b
β
p
b
<.001
-0.342
β
p
Constant
9.171
<.001
Female
1.332
.150
<.001
0.045
.031
.206
Age (in years at baseline)
0.213
.096
<.001
-0.006
-.016
.516
Socio-economic status (at baseline)
-0.044
-.041
.069
0.007
.040
.107
1.905
.171
<.001
0.110
.061
.034
0.810
.043
.127
-0.022
-.012
.654
-0.708
-.117
<.001
-0.281
-.064
.026
Change in parental mental health problems (slope) by change in family climate (slope)
2.408
.016
.550
Initial parental mental health problems (intercept) by change in family climate (slope)
-0.274
-.018
.509
Change in parental mental health problems (slope) by initial family climate (intercept)
-1.198
-.025
.401
Risk factor
Initial parental mental health problems (intercept)
Change in parental mental health problems (slope)
Protective factors
Initial family climate (intercept)
-3.259
-.277
<.001
Change in family climate (slope)
Interactions between risk and protective factors
Initial parental mental health problems (intercept) by initial family climate (intercept)
1
2
0.007
Linear regression Model A2 (n=1,643); model fit: R²=.176; F=58.177; linear regression Model B2 (n=1,643); model fit: R²=.024; F=3.701;
b=unstandardized regression coefficient; β=standardized regression coefficient
.000
.991
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Supplementary Table 6. Social support moderating the association between parental mental health problems and depressive symptoms of children and adolescents
Regression Model A31
regression Model B32
predicting initial depressive
predicting change in depres-
symptoms
sive symptoms
b
β
p
b
<.001
-0.342
β
p
Constant
8.830
<.001
Female
2.019
.227
<.001
0.047
.033
.194
Age (in years at baseline)
0.370
.167
<.001
-0.010
-.029
.235
Socio-economic status (at baseline)
-0.037
-.035
.123
0.008
.044
.075
2.006
.180
<.001
0.114
.063
.027
0.762
.040
.153
-0.072
-.044
.100
-0.928
-.138
<.001
-0.207
-.057
.043
Change in parental mental health problems (slope) by change in social support (slope)
-1.727
-.011
.706
Initial parental mental health problems (intercept) by change in social support (slope)
-1.006
-.063
.026
Change in parental mental health problems (slope) by initial social support (intercept)
0.808
.019
.481
Risk factor
Initial parental mental health problems (intercept)
Change in parental mental health problems (slope)
Protective factors
Initial social support (intercept)
-3.230
-.318
<.001
Change in social support (slope)
Interactions between risk and protective factors
Initial parental mental health problems (intercept) by initial social support (intercept)
1
2
0.329
Linear regression Model A3 (n=1,643); model fit: R²=.197; F=66.868; linear regression Model B3 (n=1,643); model fit: R²=.032; F=4.890;
b=unstandardized regression coefficient; β=standardized regression coefficient
.015
.518
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